Assuming carbon emissions damage the environment, should they be discouraged through taxation? And if so, should the tax revenue be earmarked for damage abatement, or should it be paid into general funds?

Elizabeth Kolbert, writing in the New Yorker, suggests that economic theory decides this question in favor of a carbon tax. As I pointed out last week, she’s plain wrong. As a followup to some of the discussion on that post, here’s a simple example to illustrate that no policy can be infallible:

A steel mill pollutes the air, causing $24 worth of damage to the business of a laundromat next door. (Or if you prefer, read $24 worth of expected damage to the owners of oceanfront property or farmers in currently temperate zones.)

If the steel mill is forced to bear the consequences of this damage, it reduces its output. This cuts the pollution damage by $12, and cuts the profits of the steel mill by $17.

Question: Which is the best policy?

The steel mill incurs no penalty for polluting.

The steel mill pays a tax (or fine) equal to the damage it causes; the revenue is used to reduce the national debt.

The steel mill is required to reimburse the laundromat for all damage.

Answer: It depends. Consider the following scenarios:

Scenario I. The laundromat can fully alleviate the damage (say by moving to another location) at a cost of $6. Under scenario A or B, the laundry chooses to move rather than bear $24 or $12 in pollution damage. Net cost of scenario A or B: the $6 moving cost. Under scenario C, the laundry remains. Net cost of scenario C: the $17 reduction in the steel mill’s profit. Best policies: A or B.

Scenario II. The laundromat can fully alleviate the damage at a cost of $15. Then under scenario A, the laundromat chooses to move rather than bear $24 in pollution costs. Net cost of scenario A: the $15 moving cost. Under policy B or C, the pollution damage is reduced to $12, so the laundromat chooses to stay. Net cost of policy B or C: the $17 reduction in profit. (There is also $12 worth of pollution damage, but this is offset by $12 in tax collections or reimbursement to the laundry.) Best policy: A.

Scenario III. The laundromat can fully alleviate the damage at a cost of $20. Under policy A, the laundromat moves for a net cost of $20. Under policy B or C, the laundromat reamins, for a net cost (in reduced profit to the steel mill) of $17. Best policy: B or C.

Scenario IV. The laundromat can fully alleviate the damage at a cost of $25. Now the laundromat surely never moves. Net cost of Policy A: $24 in pollution damage. Net cost of policy B or C: $17 in lost profit. Best policy: B or C, though for slightly different reasons than in Scenario III.

Moral: Policy A is suboptimal in scenarios III and IV. Policy B is suboptimal in Scenario II. Policy C is suboptimal in scenarios I and II.

Larger moral: You name a policy; I’ll find a scenario in which it’s suboptimal.

Larger moral, restated: You can’t use pure theory to settle this kind of question. Not even if you use fancy words like “Pigovian”.

78 Responses to “Carbon Tax Policy: No Simple Answers”

The environmentalist left says that conservation, green energy, and reduced development are all things that we should be doing anyway. If we transform our energy consumption to avoid global warming and the warming turns out to be a hoax, then we will have lost nothing. Or so they say.

There are extra costs when things are traded away from Pareto equilibrium. These are deadweight losses. Often associated with taxes, these also happen with externalities. I think we are simply comparing two deadweight losses here. We know there is a deadweight loss with producing carbon without a carbon tax. We know there is a deadweight loss associated with taxes. In a general case, can we say anything about the likely relative magnitude of these losses?

Well, if we get the tax at the actual social cost of the externality, we completely remove this deadweight loss. The comodity is now traded at Pereto equilibrium level, and so is efficient. Is it likely that the deadweight loss from the tax be greater than this?

Coase talked of specific cases – he was examining the interface of the legal with the economic. In these cases, there were particularly large deadweight losses. In the train case, the deadweight loss of making the train company liable for the damage (tax) was $120 and the loss was $250 – a stunning 208% deadweight loss. Whilst these extreme values are feasible in specific cases, they are hardly typical – especially when spread over millions of transactions over the whole economy.

I feel sure it must be possible to get closer to a realistic estimate of which is larger.

I think that (quite uncharacteristically for you), you’re obscuring the major point when you characterize the issue this way:

We know there is a deadweight loss with producing carbon without a carbon tax. We know there is a deadweight loss associated with taxes.

The problem is that many people will interpret “the deadweight loss with producing carbon” as the cost you impose on, say, owners of oceanfront property given that the locations of their houses, as opposed to the (possibly smaller) cost that you impose given that they have the option of moving those houses.

A reasonable characterization of Coase’s point is that Pigou calculated deadweight losses the former way, but should have calculated them the latter way. So when you simply say that we need to worry about deadweight loss, you distract attention from the importance of calculating the right deadweight loss.

It can be lttle hard seeing all the costs directly when you are juggling options.
To check Steve’s math I did deltas from a simple starting position.
I gave the mill 29 to start, the laundry 24 to start and the government 0
(an unrealistically high estimate). These numbers are chosen for convenience.
Then there is 24 in damage.
To track the effects I deducted the costs and effects from each of these.

It seems to me you’re still obscuring the point, in at least parts of your post. You say that the best policy for scenario II is A. Would you still say that if you replaced “steel mill” with “company that makes profits by punching pedestrians in the face and posting videos of the assaults on youtube”, and replaced “pollution” with “damage to pedestrians’ faces”?

The key point is that, no matter how little cost the pedestrians would incur by taking a different route, they have the *right* to walk where they want (on public sidewalks, etc.).

Philosophy of rights cannot be boiled down to economics, since it boils down so quickly to axiomatic components of ones worldview.

@5: Did you notice this was a set of counter examples? There may well be situations like the one you describe. So what? There are lots more like the one Steve describes? Kolbert et al argued that all cases are basically simple, like your punch factory. Steve shows this is clearly wrong.

It’s easy to cook up extreme and tendentious examples. Here’s mine. I open a factory making an AIDS vaccine, and it gives off sparks …

there is no substantive difference between the case i described and the case Steve described, as far as the question of whether it is possible to discern the “appropriate” policy using cost/benefit analysis is concerned.

@3. I am trying to clarify for myself rather than obscure the main points. There are costs involved with having a tax. There are costs inviolved with not having a tax. The question is which is bigger, and what does deadweight loss have ot do with it (if anything)?

Take the costs of not having a tax. We have the social cost of carbon. We also know that externalities have costs which can be desribed as deadweight loss. Is this the same as the social cost of carbon? If not, then how do they differ, and how do we calculate them?

If we take the train example, but smooth it out so we have a variable number of trains from 1 to a lot. If there were no damage to crops, we will have a supply and demand curve, which will meet at a certain point. This defines both that number of trains run and the price of them, and represents an efficient outcome. Say it is 100 trains.

Now if we include fire damage to surrounding farms and woods. This new variable will alter the optimum number and price of trains. Since running trains has a negative effect, the equilibrium number of trains is less.

If the train company is compelled to simply pay the farmer, then lets say 80 run. In a proper Coase type market, say 90 would run, since the train company would pay the farmers less to not grow crops near the track, or plant a different crop.

So actually the “True” equilibrium position would be 90 trains and the damage caused after the compensations have been negotiated. This is Pareto optimum, and is what would come about in an ideal market, if there were no transaction costs etc. as Coase describes.

What is the deadweight loss and what is the social cost? The only data we have is the damage caused and the number of trains run. We could calculate that 80 trains should run, and we know that 100 actually do run, but we cannnot calculate the 90 figure because it is the result of negotiations that have not happened.

So in this case, the damage caused to the farmers is the social cost, defined in the same manner as the social cost of carbon. The deadweight loss is the difference betweem the 90 trains (the actual market equilibrium, if we could determine it) and 100 trains (no tax) or 80 trains (with tax).

What can we know? We know that there are too many trains. We also know that if we tax the full amount there will be too few trains. We know that with no tax there is a deadweight loss, and we know that with a tax there is a deadweight loss. We still don’t know which is bigger. I see now that deadweight loss is something of a red-herring, if defined in this way (i.e. using a perfect market).

Steven’s distaste for the Kolbert article seems to her employment of usurped economic theory to support her point of view. It’s called intellectual dishonesty. Or possibly, she has never heard of Coase.

As for the punch for profits initiative, it only makes sense to apply cost/benefit analysis for things in the real world like carbon emissions. It seems almost comical to apply it to things that don’t exist. Just look at Pascal’s wager.

Whenever I see a debate like this, I wonder if we are missing the forest for the trees and just finding comfort in debating theories. I can generally agree with Landsburg’s points if the negative environmental effects of carbon are not extreme. But the science seems to show that we must take into account the possibility that climate change outcomes are extreme. If there is even a small probability of carbon emissions, on the whole, changing the habitability of the world, that must be taken into account. As Weitzman argues, if we are essentially dealing with a small probability of an infinitely detrimental effect, we cannot use cost-benefit analysis. Therefore the differences between the scenarios are negligible from a pure cost-benefit standpoint. Now, if the worst scenario doesn’t happen (which of course is likely), the difference between these scenarios does come into play, but I’m not sure the extent to which abating carbon a little would provide any more benefit that not abating carbon at all and exploiting it for all it’s worth.

I think No. 5 has a point too. In this case, the value of the punch damage would have to be whatever the victim would accept. If the company could still make a profit after paying this, then in economic terms, this is more efficient than banning punches. What I think is worrying, and I may have this wrong, is that it would remain more efficient even if the compensation were not actually paid.

No simple answers? Of course there are simple answers! Recall the words of H. L. Mencken: “For every human problem, there is a neat, simple solution; and it is always wrong.” Landsburg’s problem is he’s got a hang-up about right answers. Except perhaps for where mathematics is concerned, he seems wholly insensitive to the beauty of simplicity!

Let me add that, once again, Landsburg evaluates public policy in terms of optimizing social welfare, without regard to how that welfare gets distributed. In essence, this hypothetical ignores the idea of property rights – that is, the idea that one party has a right to a given outcome (e.g., to operate unimpeded, or to live without this kind of externality).

Within the context of this hypothetical, that seems appropriate; after all, we can hypothesize a means by which benefitted parties compensate harmed parties. Nevertheless, various commentors stumble on this idea of allocating social benefits without regard to property rights. If the externality takes the form of a punch in the face and public humiliation, doesn’t that change the analysis?

Conceptually, no. If the goal is optimizing social welfare, and we can achieve greater social welfare by punching you in the face and posting the video on YouTube, so be it. If this conclusion bothers you, it suggests that you – unlike Landsburg? – evaluate public policy on some basis other than its ability to optimize social welfare, or you believe in a kind of property right regime that would involve recognizing certain kinds of autonomy rights and compensating people for transgressions on those rights.

For what it’s worth, I value Landsburg’s propensity to evaluate public policy in terms of how well it optimizes social welfare (although I then harp on about progressivity…). For example, I believe in taxation as a tool to promote social welfare. Some libertarians do not distinguish between taxation and a punch in the face. I try not to second-guess their value system – yet I continue to support the use of taxation to promote social welfare. From their perspective, my policy preferences may not differ much from a policy of punching people in the face and posting it on YouTube.

Perhaps a minor point, but I’m having difficulty following the hypothetical.

<A steel mill pollutes the air, causing $24 worth of damage to the business of a laundromat next door. (Or if you prefer, read $24 worth of expected damage to the owners of oceanfront property or farmers in currently temperate zones.)

If the steel mill is forced to bear the consequences of this damage, it reduces its output. This cuts the pollution damage by $12, and cuts the profits of the steel mill by $17.

The consequences of the damage are $24. Face with the need to bear these consequences, the steel mill would still be liable for $12 in pollution, yet would forsake the opportunity to earn $17. Why would the steel mill make such a choice?

There are really two separate issues here, and they should not be conflated. First, what is the efficient outcome–to mitigate, abate, or do nothing? And second, is a policy needed to achieve the efficient outcome? If no policy is required to achieve the efficient outcome (for example the laundry will move away on its own accord), the effect of the policy may be (and likely will be) to reduce efficiency. Indeed, in the two party case it is likely that no policy is needed because the parties should bargain, if needed, to an efficient outcome. If the efficient policy is to abate and a policy is needed (maybe not if the laundry can sue the company for damages), the outcome can be achieved by a Pigovian tax or even by paying the company to abate.

In the real world people have an incentive to exaggerate their damages. Therefore the laundromat claims the pollution costs $24 and claims that if pollution is reduced its damage will only be $12. The steel mill claims that doing this costs $17. How can anyone verify these figures? Surely its going to cost a fortune to send outside auditors into the businesses to verify the claims? It makes more sense to have a general policy.

Also in your example, in scenario 2, you say that “there is also $12 worth of pollution damage, but this is offset by $12 in tax collections or reimbursement to the laundry. -Best policy: A” However policy A is “The steel mill incurs no penalty for polluting”, if the steel mill pays $12 tax that sounds like a penalty to me!

That’s a huge part of the point. Kolbert didn’t even attempt to talk about any figures, much less verify them, yet she yammered on about what the correct course of action “should” be, through a pretense of knowledge, rather than actual knowledge.

However policy A is “The steel mill incurs no penalty for polluting”, if the steel mill pays $12 tax that sounds like a penalty to me!

You’ve read the scenario wrong. Not tax is levied. He discusses a $12 tax when talking about the effects of policy B and C, but then concludes that policy A is better, i.e., no tax, hence no penalty.

The point is that depending on the actual costs the efficient solution may vary, no solution is correct a priori. Any one of the proposed approaches can get it wrong, depending on the facts. That’s true whether it’s easy to get the facts or not.

In every econ course I ever took, the Coase theorem was taught to be functionally applicable in only specific scenarios. Rights have to be easily definable and transferable with small transaction costs and few actors. If everybody on the world values biodiversity (for catastrophic tail-end risks, or consumption value, or just option value), then how in the world can Coase be applicable to global warming, which threatens biodiversity?
If there is no right to pollute, then the steel mill pumping out CO2 can’t possibly be expected to buy permission from every person on earth to do so. If there is a right to pollute, then every person on earth won’t pay for the steel mill to stop polluting–perfectly rational self-interested actors will free-ride, even if the efficient outcome is for everybody to pay the steel mill to not pollute.

I’m open to an explanation, though: how can Coase be applied to global pollution?

I am going to look at this from a slightly different angle. I think we can agree that pollution changes the value of the property affected. Giving a particular steel mill a right to freely pollute makes that property more valuable, while allowing the laundromat next door to be polluted lowers the value of that property. Likewise, greenhouse gas emissions alter property values — places positively affected (Alaskan tundra that is no longer frozen, maybe) are worth more, and places negatively affected (Florida coast threatened with submersion) are worth less.

Now, the Henry George Theorem states that “…under certain ideal conditions, aggregate spending by government will be equal to aggregate rent based on land value.” (see http://en.wikipedia.org/wiki/Henry_George_Theorem — In the same article, “In 1977, Joseph Stiglitz showed that under certain conditions, spending by the government on public goods will increase aggregate land rents by an equal amount.)

To grossly oversimplify things, the purpose of government would seem to be to maximize aggregate land value of the area governed. National defense raises land value (you don’t want the Chinese to grab your steel mill). Education raises land value (see what good schools do to the surrounding area). Useful infrastructure raises land value. Pollution lowers land value (bad for steel mills), but employment raises it (good for steel mills), and so on.

So if a Pigovian tax and the associated spending on public goods raises aggregate land value, it should be used. If it doesn’t, it shouldn’t (and maybe a Pigovian subsidy put in place, if that will raise the overall value of land).

(Full disclosure: I prefer Georgist and Pigovian taxes to taxes on labor, capital, or trade. Georgist taxes in particular would align the incentives of government with the incentives of the private sector — bridges to somewhere would be worth more than bridges to nowhere when it comes to tax receipts.)

The most interesting part of this discussion is how everyone assumes that the “tax” is somehow distributed to the injured party to cover the “loss.” In fact, the discussed tax is a punitive measure to prevent the harm, and is never contemplated to cover anyone’s loss. We already have a civil legal process in place that can take care of those losses in the event causation can be found. In the legal system, the injured party actually recovers for its loss, rather than the “tax” disappearing into another general fund spending cycle. The actual issue behind the “tax” is setting it at a value that prevents Steve’s analysis from ever making sense – to work as intended it must never be economically feasible to work. Therefore the steel mill must always shut down under a properly constructed tax.

(1) people, on average, would probably dislike the liability of their being punched in the face indiscriminately in exchange for the pleasure of viewing it happen to others on YouTube.

Youtube brings an extra layer of indirection since the company is not being directly paid for it, but lets pretend they are selling the footage in stores instead.

In the analogy, the company is causing $24 of pollution to particularly vulnerable people, but it can use that pollution to make products that it sells to the general public. In the punching analogy, the company is punching particularly vulnerable people in the face, but would be selling the footage to everyone, including people who know ahead of time that they are not targets for punching. So I don’t see how (1) would happen. After all, they aren’t being punched in the face–someone else is.

Furthermore, even to the people who actually are being punched in the face, once the company causes the damage and tries to sell the footage, the facial damage is a sunk cost. If they would normally prefer to buy the footage, they would be better off buying the footage and paying the sunk cost over not buying the footage and still paying the sunk cost anyway.

(2) a negative externality would be conferred upon people, on average, because they viscerally dislike being part of a society in which people can be punched in the face with impunity.

And how is this different from the original example? People also dislike being in a society where they can have their property damaged by pollution with impunity. Yet in the original example you assume that this does not happen, or at least that the externality isn’t large enough to affect the result. You should then assume the same of the punching example.

Just curious; what is your take on the so-called Pigou Club? It seems like some/most of those members should be aware that “Pigou’s analysis was ultimately superseded by better analysis — i.e. analysis that is universally acknowledged to be better by virtually every single person who has worked in the field” and leave to form a Coase Club.

The most interesting part of this discussion is how everyone assumes that the “tax” is somehow distributed to the injured party to cover the “loss.” In fact, the discussed tax is a punitive measure to prevent the harm, and is never contemplated to cover anyone’s loss.

Did you read the post before writing this? What did you think was the difference between policies B and C?

We already have a civil legal process in place that can take care of those losses in the event causation can be found. In the legal system, the injured party actually recovers for its loss, rather than the “tax” disappearing into another general fund spending cycle.

A potentially interesting point.

1. However, it is unclear that the legal system grants people remedies for all forms of harm. For example, some harms are deemed to be covered and redressed by regulatory schemes and are thus beyond redress through the courts.

2. The idea that a judge will order compensation “in the event causation can be found” is somewhat self-referential: Does a judge find liability on the basis of finding causation – or find causation in order to justify a finding of liability?

Legal “causation” is rarely a matter of fact alone, but rather a mixed question of fact and law. For example, am I entitled to unemployment compensation if I quit my job? If my girlfriend gets transferred out of town and I’m moving to be with her, the judge is likely to conclude that I voluntarily separated from my employer and thus I’m not entitled to unemployment compensation. But if my SPOUSE gets transferred and I’m moving to be with her, then the court is likely to conclude that my separation from employment was involuntary and thus I am entitled to unemployment compensation. The judge’s finding about what “caused” my separation from employment is a function of the conclusion the judge draws about my entitlement to unemployment benefits, not the other way around.

3. That said, when a judge DOES find that a defendant is liable, the amount of the liability can be reduced if the plaintiff failed to take advantage of opportunities to mitigate damages. If the laundromat sued the steel mill for damages in Landsburg’s hypothetical, the amount of those damages would presumably equal the amount required to “fully alleviate the damage,” up to a maximum of $24.

Would this type of compensation result in sub-optimal social outcomes under any variant of Landsburg’s scenarios? In this stylized world, perhaps the civil liability system provides the optimal public policy here.

I accept your modification that they were selling the footage in stores instead of posting it on YouTube.

However, punching inc. is not punching “particularly vulnerable people” in the analogy. If we assume punching inc. is an international conglomerate (and I don’t see why we shouldn’t), everyone has the potential to be punched. And likewise everyone has the opportunity to purchase the footage in stores for their amusement. This seems like a cost/benefit problem. 5′s silly point was that his face-punching hypothetical discredits such a cost/benefit analysis.

As for (2), there’s a difference between living in a society where people dislike something on principle (which corresponds to people being punched in the face indiscriminately) and living in a society where people dislike something because it ACTUALLY damages society (which corresponds to pollution). I can’t think of anyone who dislikes pollution on principle; they dislike the damage it causes.

Is this an error? Same question as nobody.really in #13 — in all scenarios where the steel mill has to pay the costs of pollution, they can either pay $24 in pollution costs, or if they reduce their output, they still have to pay $12 in pollution costs plus they lose $17 in profit, for a total loss of $29. Thus with the numbers given, it would never make sense for the mill to reduce their output. Am I missing something?

Also, in Scenario I, under policy C, rather than reimbursing the laundromat for pollution damage (either $24 or $12, depending on whether the mill reduces output), wouldn’t the steel mill just pay the laundromat $6 to move?

Thus in the original problem statement:

“A steel mill pollutes the air, causing $24 worth of damage to the business of a laundromat next door. (Or if you prefer, read $24 worth of expected damage to the owners of oceanfront property or farmers in currently temperate zones.)”

it seems these are fundamentally different problems — in the former case, the parties can negotiate the lowest-total-cost solution no matter who is liable for what, but in the second case, the bargaining is impractical with so many affected parties. (This is all part of the Coase Theorem, isn’t it?)

So to make the problem a real model of the pollution policy question, I presume you have to add the restriction that you’re not allowed to negotiate cross-payments like that (other than government-mandated fines or reimbursements for pollution damage).

D. The steel mill pays a tax (or fine) equal to the “harm” it causes; the revenue is used to reduce the national debt. “Harm” is defined as the cost of the least costly option available to the victim, counting preventative measures.

I couldn’t directly use the given scenarios, as the “harm” varies, thus the tax varies, and thus the steel mill’s reaction to having to pay the harm varies. But it can be made to work by expanding the set-up to:

The steel mill can only produce at full or half capacity, which cause either $24 or $12 in damages. Its profit is $5 higher at full capacity than at half. This, it cuts production in half if this saves $5 or more in taxes.

—

Scenario I: The harm at full (half) capacity is $6 ($6). Production is not cut, and the laundromat moves. Net cost: $6 in lost profits. Plans and A, B, and D are optimal.

Scenario II: The harm at full (half) capacity is $15 ($12). Production is not cut, and the laundromat moves. Net cost: $15 in lost profits. Plans A and D are optimal.

Scenario III: The harm at full (half) capacity is $20 ($12). Production is cut, and the laundromat does not move. Net cost: $17 in lost profits. Plans B, C, and D are optimal.

Scenario IV: The harm at full (half) capacity is $24 ($12). Production is cut, and the laundromat does not move. Net cost: $17 in lost profits. Plans B, C, and D are optimal.

So plan D is optimal in all four scenarios.

In fact, it should always be optimal. Both the laudromat and the mill have perfect incentives, so their rational choices are the efficient ones.

Does the laundromat *also* pay a tax equal to the harm it causes? E.g. if the laundromat, by virtue of its existence, causes the steel mill to have to pay a tax of $X (equal to the harm it causes to the laundromat) (and if the steel mill has no cheaper alternative to paying this tax), does the laundromat then have to pay a tax of $X?

Consider this scenario: A rabbit farmer and a lettuce farmer are located next door to each other. As a result, $10 worth of lettuce is destroyed each year. Either party could avert the damage by moving away at a cost of $8. I take it that under your proposal, they each pay a tax of $8. What if this puts them both out of business?

Alternatively, if you tax only the rabbit farmer and not the lettuce farmer, then you create an artificial incentive for people to take up lettuce farming rather than rabbit farming — whereupon the world gets too much lettuce and too few rabbits.

No. They both pay total costs equal to the harm they cause. The mills pays in tax dollars, and the laundromat pays in rewashing expenses.

It would be double-counting to say the laundromat is causing costs both due to the tax and due to rewashing expenses. The tax is only a cost if it causes less production, but less production now means fewer rewashing expenses. Furthermore, less production only happens if this is less costly than the rewashing expenses.

> Consider this scenario: A rabbit farmer and a lettuce farmer are located next door to each other. As a result, $10 worth of lettuce is destroyed each year. Either party could avert the damage by moving away at a cost of $8. I take it that under your proposal, they each pay a tax of $8.

Similarly, here, if the government does nothing, the rabbit farmer avoids all costs. No tax is needed to make the lettuce farmer pay for the costs of his choice. So my plan is to tax only the rabbit farmer.

Thinking more about rabbits and lettuce showed me an assumption that I didn’t realize I was making.

I’m assuming that first, the mill adjusts their behavior based on the laundromat’s current behavior, and next, the laundromat adjusts theirs, and not further changes occur. I don’t have a numerical example to back this up, but I bet there are set ups leading to “playing chicken” if the decisions are simultaneous. (Or some variant of chicken where swerving late is almost as bad as crashing.) This sounds very likely to be inefficient.

If ordered decisions are a necessary premise, then I’m not making an argument based on pure reason, but also on specifics of the circumstance.

This is probably a true premise for the carbon tax, but here, there’s more than one “mill.” I can’t think of any reasonable way to extend my tax to multiple mills when harm is a non-linear function of pollution.

Jeffrey: Yet another problem with your solution is that it requires the policymaker to know a lot of detail about amelioration costs. This is often implausible, especially if there’s no history of amelioration and hence nothing to observe.

Of course my numerical examples also assume full knowledge of amelioration costs, but that’s part of the point — we, the omniscient observers, know these costs, but the policymaker in the problem often doesn’t; therefore any policy at all can easily be wrong.

As I understand it, Coase showed that if transaction costs are zero, the efficient result will always happen whoever we decide to “blame”. Benefits will always be negotiated to result in the same social outcome. So if you make the mill compensate the laundry,the mill can negotiate with the laundry to reduce the harm and so reduce the compensation. If you don’t make the mill compensate the laundry, the laundry will negotiate with the mill to reduce the harm, and you will end up with the same total social benefit. This does not mean that it does not matter to the laundry and the mill, each will pay different amounts, but the total social benefits will be the same.

That is if negotiation is possible. What if it is not?

Faced with a problem such as global warming, we must decide what to do – remembering that doing nothing is a decision too. We can either tax or not tax the externality.

If we do not tax the externality, we know we increase harm. If we do tax the externality, then cheaper damage limiting moves may not be made. Which is the greater? We cannot simply say that since we do not know, we do nothing, as that is assuming that the foregone damage limitations would have been cheaper.

So it comes down to whether it is cheaper for emitters of carbon to reduce emissions, or victims of warming to ameliorate the harm. We must decide.

On the face of it it seems obvious that emitters can more easily reduce emissions. The damage will be widespread and affect everybody, although some more than others. The effects will include more extreme weather, which will be local in effect but global reach. This sort of thing is very expensive for harm reduction as you do not know where it will happen. Heatwaves kill thousands, and we can expect this to increase. This is very expensive to ameliorate. Sea level rises will threaten many cities. Much of the damage will occur in random extreme events, like the “superstorm” in New York. Re-situating a new city further inland will not be as expensive as replacing New York at a stroke, but it will come with large costs. Rainfall patterns will change, so populated areas will not be able to support their populations. Other areas will become more productive, but the costs of re-establishing new populations in the new productive areas will be vast, since they are in different countries, and continents. Adapting to the change involves wholescale moving of billions of people. This is not going to be cheap.

On the other hand, reductions in emmissions can be made with very little change to lifestyle and very little cost. Fuel economy of new cars in UK is twice that in the States, and that does not seem to have destroyed the way of life. This perhaps is the clincher. The social cost is rising. If we reduce emmissions, we slow down that rise in cost. Amelioration is unlikely to get cheaper.

There is no incentive to develop new energy forms if the real costs of fossil fuels are not paid. This means that the social cost continiues to rise, whereas if we have the tax, new form of energy can compete, and innovation will further reduce the costs. Currently, the Govt. attempts to get round this with subsidies, but how much better a tax and allow the market to decise on which technology to pursue?

Given what we know, it seems inconceivable that harm reduction could be the cheaper alternative to emmission reduction. A simple way to think of it is that emmission reduction does not change where we are now, harm reduction does. It is overwhelmingly likely that the option involving least change will be the cheaper.

35: “Similarly, here, if the government does nothing, the rabbit farmer avoids all costs. ” I am not sure why, as the costs are symmetric. I gather you think that the rabbits are *causing* the damage so the the situation is assymmetric even if the costs are symmetric. Is that right?

27: As stated, it was a comment concerning the discussion. Your original posts are interesting, but the discussion is where the real fun is. As such, the focus was on taxation and its use as recompense for loss while the reality is that an offset tax is created to preclude the reasonableness of an activity.

To answer your question in the post, C. A is at least politically impossible, and amounts to a license to pollute – imagine Love Canal or other media firestorm. B is a false assumption that the tax is in the amount of damages while it actually is a barrier to entry/continuation. C covers damages, and has a punitive/exemplary damages component which would make your caclulations unpredicable thus serving both a compensatory and preclusive function.

39. Without either Govt action OR liability OR the possibility of negotiation, the lettuce farmer suffers all the loss and the rabbit farmer none. I presume this is what Jeffrey means. The lettuce farmer will choose to accept the $8 loss of moving rather than the $10 loss of lettuce. Total social cost = $8

If we tax the rabbit farmer the total damage of $10, then HE will suffer all the loss. He will choose to take the $8 loss of moving rather than the $10 loss of the lettuce eating tax. Total social cost = $8. No difference with or without the tax.

If we allow negotiation, then in the frst case, the lettuce farmer could offer the rabbit farmer money to move his rabbits. The costs of moving the rabbits is the same as moving the lettuce, so there is not bargain to be made in this situation.

If the rabbits could be moved for $4 and the lettuce for $8, then we have an interesting situation. If we do not make the rabbit farmer liable, then the lettuce farmer bears all the loss. Instead of letting $10 lettuce get eaten, he could move for $8, or he could pay the rabbit farmer a smidge over $4 to move his rabbits. Total social cost = $4, paid for by the lettuce farmer.

If we make the rabbit farmer liable, then he suffers all the loss. Rather than let his rabbit eat $10 woth of lettuce, he will move them at a cost of $4. The same outcome in social cost whether we make the rabbit farmer liable or not.

To address the logical issue. Simple supply and demand reasoning shows that if we posit an external cost (whether damages or mitigation costs), there exists a small Pigovian tax that can increase economic efficiency (reduce the deadweight loss of externality). So what am I going to believe, SL’s counter-examples or my lying supply and demand diagrams?

The answer is that SL’s counter examples are not marginal. There exists a Pigovian tax, but it is at a lower rate than the one being considered. To see this note that at a market equilibrium, firms are maximizing profit so the profit function is locally flat with respect to small changes in output. In other words, for a marginal change, the reduction in profit from a small reduction in output is second order small and can be treated as zero, whereas as the effect on damages is of first order.

I know this is esoteric, but what else do you expect on this site?

For the record, I agree that any real world policy should have the right benefit cost calculations. I am just arguing the theoretical point here.

37: “Yet another problem with your solution is that it requires the policymaker to know a lot of detail about amelioration costs.”

Plan B requires knowledge of the damage that will be caused, while Plan D also requires knowledge of the preventive costs. While knowing two things will always be harder than knowing one thing, in some cases it’s not much harder.

For example, I think it would be drastically easier to estimate the cost of relocating a beach home than to estimate the damage to this beach home caused by one ton of carbon consumption.

@ Ken B 39: “I am not sure why, as the costs are symmetric. I gather you think that the rabbits are *causing* the damage so the the situation is assymmetric even if the costs are symmetric. Is that right?”

I’m not meaning to assume that the rabbits are any more to blame than the cabbages.

There is an asymmetry in what happens in the absence of government intervention. The default result is not $5 of damage to the rabbits and $5 of damage to the cabbages; the default bearer of all costs is the cabbage farmer. Thus, to make actors bear the costs of their choices, taxing the rabbits is needed while taxing the cabbages is redundant.

31, 38, 41 – I too recall Coase as suggesting that pre-assigning rights ultimately determines who pays whom, but not who does what, assuming negotiation is possible based on the relative costs of alleviation (which clearly gets messier the more parties that are involved). Does this suggest policy B is generally suboptimal because it precludes negotiation? I would note B is never “more optimal” than one of the other policies, even without allowing for negotiation.

For those (5 & 12) suggesting the analysis “ignores rights”, I think if you prefer you can start with, say, policy C (which assigns a property right to the Laundromat) or A (which does not), and then work through the scenarios. E.g. the Laundromat moves if that costs less than $17, and gets paid either $0 (under A) or something more than $6 or $15 but less than $17 (under C); the mill cuts back if the cost of moving the Laundromat is more than $17, and gets paid either $0 (under C) or something more than $17 but less than $20 or $24 (under A). Or something like that. Again not sure how B fits into this.

@45:
My basic take is, worth paying attention to, not worth doing anything very costly yet.
I laid out my case in a very long comment here not too long ago so won’t repeat. Briefly: the costs should be spread over the future, where they can be minimized and spread more sensibly; the claims about the damage and the certainty of it are possibly overblown: we’ll know more later.
I don’t think it a sham; I do think there has been a lot of irrational fear mongering.

1. Per Coase, we can achieve optimal social outcomes if we a) have clearly assigned property rights – including clear rights about pollution — and b) transaction costs are sufficiently low. The manner in which property rights are allocated will alter the ultimate allocation of social benefits – but not the total social benefits achieved.

2. Arguably, US civil (tort) liability laws are designed to promote optimal social outcomes, in that they may require a defendant to compensate a plaintiff for the harm the defendant “caused” offset by the amount of harm the plaintiff incurred by failing to take action to mitigate damages. Alas, few people regard the tort system as imposing low transaction costs.

3. Where transaction costs are high – say, when seeking to compensate for the harm of global climate change – societies may institute proxy means (such as taxes) for allocating costs related to externalities. Landsburg notes that these proxies may not achieve the same level of social benefits as the idealized Coase model. However, the failure to adopt the proxies may also fail to achieve the optimal level of social benefit.

CO2 is not a pollutant and none of the climate models has ever predicted the current 16 year period of non warming. Also the crop yields would be lower under the preindustrial levels of CO2 – so there is a huge positive externality. No doubt there is some human caused warming, but the rest of the ‘science’ is quite doubtful. People react to incentives and there is a lot of money at stake to be not paid out to different groups if there is no climatic threat..

If it is going to destroy the world then it seems that the politically possible solution is best even if it is far from optimal.

This is pure poppycock. The worst case scenario of “doing something” is to end up with a brutal oppressive global government, not just restricted to certain places, like 20th century Russia and China, as well as the modern day north Korean peninsula. Since these brutally oppressive governments have actually come into being and killed hundreds of millions of people, whereas none of the horrible affects of global warming are anywhere to be seen, it’s clear that those who call for “something to be done” are myopic in the extreme.

In other words, if the world ends due to the actions mankind, it’s faaarrrr more likely to occur due to aggressive over sized government, rather than the usage of fossil fuels.

Landsburg notes that these proxies may not achieve the same level of social benefits as the idealized Coase model.

That’s beside the point. The point is that these proxies may not achieve the same level of social benefits as alternative policies, including (but not limited to) doing nothing.

Perhaps we have different understandings of the point.

When I read Landsburg’s hypotheticals, I draw the conclusion that there are various policies that might produce optimal outcomes, if only we could tailor policies to each individual’s circumstances on the basis of highly exacting data. Put another way, I conclude that no public policy is likely to achieve those kinds of results, and thus this analysis is perfectly indeterminate.

Given that econ theory seems to provide no practical way to know which public policy would produce the greatest aggregate social benefit, what do you do? You could adopt a heuristic that says, “Do nothing unless justified by econ theory.” Or you could adopt a heuristic that says, “Do what seems intuitive to you unless contradicted by econ theory.” Because I do not regard econ theory to be the sole basis upon which to evaluate public policy, I favor the latter heuristic.

While Elizabeth Kolbert may be insufficiently humble in her policy recommendations, no one has identified policies that we can show would produce better results. If her proposals strike you as more intuitively appealing than the status quo, I can’t fault your policy choice. No, I couldn’t justify that choice based solely on econ theory. By the same token, nor can I justify the status quo. To me, THAT is the point.

However, punching inc. is not punching “particularly vulnerable people” in the analogy… everyone has the potential to be punched. And likewise everyone has the opportunity to purchase the footage in stores for their amusement.

In the original version, the company causes damage to people next door or to people in coastal zones, not to the general public, which is analogous to punching vulnerable people.

There’s also still the sunk cost problem: once everyone has been punched, they may as well buy the footage (assuming they would otherwise buy such footage) because the cost of being punched is a sunk cost and cannot be avoided by not buying the footage. (And if they want to refuse to buy the footage to discourage future punches, you now get a collective action problem.)

As for (2), … I can’t think of anyone who dislikes pollution on principle; they dislike the damage it causes.

Since we’re running a cost/benefit analysis, people’s dislike of being punched in the face implies that being punched in the face has a cost.

At any rate, the original scenario is inconsistent. For instance, it includes the case

Scenario I. The laundromat can fully alleviate the damage (say by moving to another location) at a cost of $6. Under scenario A or B, the laundry chooses to move rather than bear $24 or $12 in pollution damage. Net cost of scenario A or B: the $6 moving cost. Under scenario C, the laundry remains. Net cost of scenario C: the $17 reduction in the steel mill’s profit. Best policies: A or B.

If the direct damage is $24 and the laundromat can alleviate it for $6, then scenario C will not result in the steel mill being unable to make $17, because the laundromat owner would negotiate with the steel mill and say “if you pay me some amount which is greater than $6 and less than $17, I will sell you the right to cause the damage.

“There is also $12 worth of pollution damage, but this is offset by $12 in tax collections.”

$12 in tax collections should more than offset $12 worth of pollution damage because the increase in tax collections will let us reduce distortionary taxes.

If we take this into account, Policy B should now dominate Policy C and fare better against Policy A. The point still remains that theory can’t tell us which policy is right. However, the probability that B is the right policy is higher when we make the model more realistic.

@46 “not worth doing anything very costly yet.” We are back here again – what does “very” mean?

It seems that a tax proportional to the social cost would not be “very” costly. It is about $0.03 per liter of gasoline. Of course, the tax will promote people to take action to reduce the effects of the tax, by innovating in alternative technologies, so the damage from the tax will be reduced in the same way as the damage from the warming.

@50. You suggest that a 3c/L tax is roughly equivalent to brutally oppresive global Government? I think we can see who is scaremongering here.

@42. This is what I have been fumbling around. The marginal case will be improved with a tax. That tax must lie somewhere between the social cost of the damage without amelioration and zero. It will not be zero unless the damage limitation is costless. Since we must come up with an estimate (even if it is zero), we should pick the best we can. If the variables are impossible to calculate, how about splitting the difference and taxing at 50% of the social cost? The worst you can be is 50% off in this case.

KenB – care to be a little more specific?
I suppose on a grand scale, this is very much like the rabbits and the lettuce. A “justice” approach may say that since the developed countries have actually put most of the carbon into the atmosphere, they should pay for the damage. The counter argument is that the third world is just as much causing the harm by having coastal cities and depending on the monsoon in the first place. There is insufficient incentive currently for the developed world to stop putting more CO2 into the atmosphere.

I think Coase did not consider the marginal value of money. A dollar is worth more to poor people than rich people. The most efficient outcome in his examples results in the same overall social value only if we value say the rabbit farmer and the lettuce farmer equally. If the dollar is worth more to the lettuce farmer, then it does matter who we make liable.

Another issue is “moral hazard”. If we do not make people liable, they have a great incentive to continue harming where they could easily prevent it.

It appears to me that a lot of nonscientists are claiming that the current understanding of the experts is wrong.

The experts appear to be saying that AGW is worse than they thought just a few years ago. The World Bank came out with a report saying that AGW appears to be worse. The New York Times had an article a few weeks ago pointing out that the models that best predicted current humidity levels are the ones that were forecasting the worst AGW.

I still haven’t heard a reasonable explanation for why a conspiracy among climate scientists makes any sense at all. If there were a conspiracy then scientists would have a big incentive to prove that AGW doesn’t exist. Exxon has a huge stake in AGW. Why can’t anyone prove that AGW is wrong?

Isn’t it a reasonable assumption to believe that AGW is real because smart people with a lot of money have huge incentives to prove it wrong and have not been able to come up with any reasonable counter argument?

@60 If the changes in climate are not caused by greenhouse gases and are caused by sunspots or by the amount of sand on the Jersey shore then someone could show there is a correlation between something OTHER than greenhouse gases and the increase in temperatures.

All of the other theories have not stood up to rigorous analysis.

Maybe there is another cause but no one has any idea what the cause might be.

I was referring more to the idea that once the discussion morphs from warming into “change”, e.g. flood and drought, it becomes difficult to see what sorts of correlations might be used for testability

I think Coase did not consider the marginal value of money. A dollar is worth more to poor people than rich people.

By this reasoning the amount of the carbon tax shouldn’t actually depend on the damage caused at all–even a carbon tax that pays for nonexistent damage would transfer money from rich people to poor people for whom the money has more marginal value. Indeed, this reasoning justifies taxes whose size is limited only by whether businesses are completely destroyed by them.

I still haven’t heard a reasonable explanation for why a conspiracy among climate scientists makes any sense at all.

Your post is the first appearance of the word “conspiracy” on this page (aside from the link to the Volokh Conspiracy).

Just about everyone here (if not everyone, period) hasn’t been saying that there’s a climate science conspiracy or that global warming is fake. There’s a common fallacy “something must be done, this is something, therefore we must do this”. It is constantly used for global warming. Whether global warming exists is completely different from whether any particular anti-global-warming measure is a good idea.

I think Coase did not consider the marginal value of money. A dollar is worth more to poor people than rich people.

By this reasoning the amount of the carbon tax shouldn’t actually depend on the damage caused at all–even a carbon tax that pays for nonexistent damage would transfer money from rich people to poor people for whom the money has more marginal value.

Coase’s thesis is about economic efficiency. My understanding is that efficiency analysis gives us the best understanding of how wealth moves around and is a necessary precursor to talking about wealth distribution.

I was discrediting the notion that the punching analogy was a good objection to cost benefit analysis. I think we agree that it is perhaps a well-posed cost/benefit problem. It’s a rather poor analogy to the original carbon emissions problem.

@neil Wilson

Would we not to at least consider passing the costs of global warming to the vastly wealthier and vastly more populous world of the future which is comprised of completely of people who are complete strangers to us?

I was discrediting the notion that the punching analogy was a good objection to cost benefit analysis. I think we agree that it is perhaps a well-posed cost/benefit problem.

My cost/benefit remark was addressing your second objection. Your second objection implied that it was not a well-posed cost/benefit problem. Specifically it contrasted punching with pollution by claiming that people object to punching for reasons other than cost.

It’s a rather poor analogy to the original carbon emissions problem.

Your objections to the analogy were based on
1) It limits who can get punched in the face and that is unlike the original problem (to which I pointed out that the original problem does in fact limit who is damaged by the factory).
2) People object to punching on principle, while they only object to pollution because of the damage (to which I pointed out that since it is a cost/benefit problem an objection “based on principle” is actually an objection involving damage).

Regarding marginal value of money, it really only comes into play if you consider the “justice” argument. The efficiency argument is incomplete. I am mixing my principles – not that important for now.

Now I have thought some more, I think the moral hazard argument is more important. Take the case with no liability.

The lettuce farmer was there first. He had no way of knowing there would be rabbits arriving later, and so has no reason to plant his lettuces elswehere.

Now arrives the rabbit farmer. He sets up next to the lettuces, as this is the best location for him. His rabbits cause $10 worth of damage. The lettuce farmer pays him $8 to move or moves his lettuces – total social cost $8.

Consider the case where we make the rabbit farmer liable. He does not set up next to the lettuces, but in the place he moved to in the first example. This may be slightly less good, but if we consider that most of the $8 was moving cost – say $7, then the total social cost is $1. In any case, the cost must be lower.

Liability makes a huge difference.

If we do not apportion liability, then there is no incentive for the party to take the lower social cost alternative in the beginning.

It still works if the rabbit farmer was there first. If the lettuce farmer sets up next to the rabbits, he will not get compensated. He has a choice – pay the rabbit farmer to move, or more likely set up in the place it would have cost him $8 to move to. Only a marginal social cost.

Thus making the later party liable will in some cases reduce social cost, but according to Coase it can never increase it.

Marginal value again. Coase showed it makes no difference to social welfare whether liability is placed on a particular party. However, it does make a difference to the parties concerned. As a matter of policy, would it not be a good idea to try to ensure the benefit went to the party that would benefit most? In most cases this is impractical, but for global scale happenings, it may be worth the effort.

First: Let me point out that the rabbit/lettuce example is in many ways offtopic here, because carbon emissions generally involve high transactions costs (how do we get all the emitters and all the breathers into a room together?) while a single pair of farmers, living next door to each other, generally have low transactions costs (which we can treat as zero for illustration).

The easy observation is that giving Larry the right to compensation for damage to lettuce is equivalent (in efficiency terms) to giving Rachel the right to raise rabbits with abandon.

The slightly more subtle observation is that awarding a right to *Larry* is not the same thing as awarding a right to *lettuce farmers in general*, and awarding a right to Rachel is not the same thing as awarding a right to *rabbit farmers in general*. For one thing, the latter automatically increases transactions costs: Larry has to negotiate now not just with Rachel but with every potential rabbit farmer. For another, the latter changes the incentive to *become* a lettuce farmer or a rabbit farmer in the first place; the former doesn’t (since there’s no such thing as an incentive to “become Larry”).

So now the question is: Given zero transactions costs between pairs of individual farmers, is there an efficiency difference between a liability rule that favors lettuce farmers in general and one that favors rabbit farmers in general? Answer: It depends.

There are some circumstances in which it is true though non-obvious that the two liability rules are equivalent. But there are others in which they aren’t equivalent. In particular, H. A. Frech, in a beautiful paper from the 1970′s, gave an example involving steel mills and laundromats in which a) a liability rule favoring steel mills is inequivalent to a liability rule favoring laundromats, b) neither rule is efficient, and c) it is impossible to devise *any* efficient liability rule.

@71 – thanks for the distinction between individuals and classes it does make a difference. In my simple example, it is only the chronological events that lead to a desirable outcome. Giving rights to lettuce farmers would back-fire if the rabbit farmer were there first. This makes it difficult to arrive at a general rule except perhaps that making someone liable for damages that they knew about in advance would be a good idea.

H. A. Frech, in a beautiful paper from the 1970′s, gave an example involving steel mills and laundromats….

I WONDERED how Landsburg arrived at an example using steel mills and laundromats.

Let me point out that the rabbit/lettuce example is in many ways offtopic here….

And I wondered about this example even more. Because the classic example is so similar: farmers and ranchers.

To what extent are property rights “natural” and to what extent are they socially derived? A study of fence-in/fence-out laws provides some insights. Initially the states of the Midwest favored fence-out laws — that is, we had wide-open spaces, and if a farmer wanted to keep cattle out of his fields he had to erect fences. But as farmers gradually came to dominate any given jurisdiction, the laws would change to impose upon the rancher the duty to keep cattle out of the farmer’s field — in essence, to fence his cattle in.

Coase would presumably recognize each remedy to this externalities problem. And presumably we would recognize that the choice of how to allocate benefits and burdens reflected not “natural rights,” but social power.

“First: Let me point out that the rabbit/lettuce example is in many ways offtopic here, because carbon emissions generally involve high transactions costs”
Well, it is a starting point – I think it shown that there IS some theoretical equilibrium that would arise IF everyone could trade, and shows that in this case liability does not (always) matter. It is this equilibrium we move towards or away from when we choose to enforce liability or not.

Is it the case that the deadweight cost of each action is the difference between this equilibrium and the actual result? Thus an incremental tax would take us towards this point, but somewhere along the line we would pass it, and start accumulating costs on the other side. Or have I got this wrong.

What should one should do as a policy maker? There is no theoretical basis for deciding, but taking no action is effectively making an extreme choice. If I have it right, we know that a small tax would be an improvement, given that there is a social cost.

@71, doesn’t the rule also have to specifically cover an activity that is currently occurring (not sure how to formalize that)?

i.e. if the liability rule states that Larry is responsible for any damage to his lettuce caused by Rachel’s rabbit farming activities, that already changes the incentives for Rachel to setup or expand rabbit farming activities next to Larry? So the rule would have to be restricted to cover only currently occurring lettuce/rabbit farming activities?